The quality of images taken under water is vital to many military and civilian applications involving mine detection, diver visibility, and search and rescue. The ability to obtain better images at greater distances has often been a central goal of underwater imaging projects. Unlike in the atmosphere, where visibility can be on the order of miles, the visual range in the underwater environment is rather limited, at best on the order of tens of meters, even in the clearest waters. This is the result of the combined attenuation effects from both absorption, i.e., photons being absorbed into water molecules, phytoplankton cells, and detritus, and scattering, i.e., photons being bounced away from the original path into different traveling directions. It is mostly the effects of scattering by water and particulates that make the water look dirty or less transparent, resulting in a blurred image seen by human eyes and recorded by cameras.
Image quality representation is an interesting and important research subject in digital image processing, especially with the rapid expansion of digital cameras, scanners, and printers into the everyday life of most households in recent years. Such devices would be of little use if they did not provide an acceptable representation of the subject of the image that was suitable for its intended purposes. The ability to objectively differentiate qualities amongst different images is critical in digital image processing, both for post-processing restoration of degraded imageries and in real-time imaging enhancement.
A widely used criterion to evaluate image quality is the sharpness of the image, which represents the ability to reproduce details of subjects in the image. This directly affects the image's resolution, which is often expressed in terms of smallest pixels or the inverse of the highest spatial or angular frequency of the imaging system. Another related quality measure is the contrast of an image, and is usually determined by the difference between lighter and darker areas, normalized by the averaged brightness of both areas. See W. Hou et al., “Why does the Secchi disk disappear? An imaging perspective,” Opt. Exp. 15, 2791-2802 (2007) and H. H. Barrett et al., Foundations of image science (Wiley-Interscience, Hoboken, N.J., 2004).
The most significant contributor to image blur is scattering, especially multiple scattering, where the path of a photon changes several times before reaching the receiver. The reduction in image quality due to scattering is two fold. Firstly, the un-scattered direct beam which contributes to the sharp part of the image is correspondingly reduced. Secondly, the scattered photons help to brighten the previously darkened area thus reduce contrast. Adding absorption on top of scattering, the reduction in signal can be so great that the electronic noise of the system becomes a factor, further complicating the issue.
The amount of blurring in an image can be described by how much blur a point-source will introduce over the imaging range. This property is the point-spread function (PSF) of the imaging system. The Fourier transform of the PSF is known as the optical transfer function (OTF), generally for incoherent imaging without considerations of phase information, the magnitude of OTF, referred to as the modulation transfer function (MTF), often is used. The OTF (or MTF) describes the frequency response of signals over transmission range, or how fast the details of an image degrade in a given environment. To compensate for blur and improve imagery effectively, it is critical to incorporate knowledge of the optical properties of the water to better model the degradation process.
Studies have been done regarding image degradation through the atmosphere transmission. However, unlike the underwater environments, degradations of the image quality by the atmosphere are most dominantly caused by turbulence under optimal conditions, although scattering by particles and aerosols also play a minor role. Better restoration in astronomy or reconnaissance applications can be obtained with knowledge of the modulation transfer functions. See D. Sadot et al., “Restoration of thermal images distorted by the atmosphere, based on measured and theoretical atmospheric modulation transfer function,” Opt. Eng. 33, 44-53 (1994); and Y. Yitzhaky et al., “Restoration of atmospherically blurred images according to weather-predicted atmospheric modulation transfer functions,” Opt. Eng. 36, 3062-3072 (1997).
The scattering behavior is different in the situation of natural waters, where strong forward scattering dominates. For example, in coastal waters, especially those inside a harbor, or in estuary areas such as Mississippi, visibility can quickly reduce to zero in a matter of a few feet. The same applies to regions of strong re-suspensions from the bottom, both in coastal regions as well as in the deep ocean. The images obtained under such conditions are often severely degraded or blurred. The extent of such blurring can be described by the PSF (MTF in frequency domain) of the medium which includes water itself, constituents within such as particulates (both organic and inorganic). See W. Hou et al, Opt. Exp. 15, supra. Theoretically, such effects can be compensated by deconvolving the PSF of the medium from the resulting images. See H. H. Barrett et al., supra.
Although traditional image enhancement techniques can be applied to imagery obtained from underwater environments, their effectiveness is considerably limited because they do not take into account the processes that lead to the degraded images, which involve in-depth understanding of the optical properties of the medium.
In theory, complete and accurate restoration can be achieved to high fidelity with known system functions and noise characteristics. In reality, the effectiveness is often hindered by errors associated with the modeling efforts deriving the MTF and the approximations applied. The noises from measurement results are also part of the mix. Additionally, due to the small incremental quality improvements in restoring degraded images, it is hard to judge if one restored result is better than the other, which is critical in an automated process. For these reasons, it is necessary to develop a method to determine objectively the quality of resulting image that associates correctly with the environmental properties. This, in turn, can be used to better determine the more specific issues affecting imaging in underwater environment, namely, low lighting thus low signal to noise levels, fluctuations caused by the medium, and multiple scattering contributions.
Recent advance of wavelet research provides an excellent tool for this purpose, as wavelets are multi-resolution in nature. See G. Kaiser, A Friendly Guide to Wavelets, (Birkhauser, 1994).